The United Nations, meanwhile, said on June 24 that at least a 1,075 people -- most of them civilians -- have been killed in fighting and other violence in Iraq in June alone -- the highest death toll since the U.S. military withdrew from the country in December 2011.

The UN's estimated toll includes victims of bombings as well as the alleged executions of civilians, police, and military recruits as Sunni-led militants seized swaths of territory in Anbar Province and to the north of Baghdad.

The Islamic State in Iraq and the Levant (ISIL), an Al-Qaeda splinter group (also known as ISIS), claimed that it executed more than 1,700 Shi'ite military recruits after capturing the city of Mosul earlier in June.

Kerry traveled from Baghdad to meet Barzani in Iraq's northern city of Irbil on June 24 in a bid to encourage the formation of a new, more inclusive Iraqi government.

The Kurdish leader said at the beginning of the meeting that "We are facing a new reality and a new Iraq," adding that it was "very difficult" to imagine Iraq staying together.

Kerry said during his talks with Barzani and other Kurdish officials that "the government formation challenge is the central challenge" in Iraq.

On June 23, al-Maliki, who has been widely criticized for fueling sectarian tensions in Iraq by failing to give an adequate stake of power to Sunni and Kurdish representatives -- told Kerry he would meet a July 1 deadline to form a new inclusive government.

On June 24, ISIL militants and allied Sunni tribal militia fighters continued battles aimed at consolidating control of territory they have seized recently.

Iraqi military officials have denied claims by ISIL that it fully captured the country's main oil refinery at Baiji near Mosul on June 24.

Government forces say they carried out a series of air strikes on June 24 against militants who are besieging the refinery, claiming that dozens were killed. It was not immediately possible to verify those casualty claims.

Meanwhile, the Pentagon said 90 U.S. military personnel have arrived in Baghdad to help Iraq security forces set up a joint operations center. They joined 40 personnel already on the ground.

The new deployment follows a diplomatic agreement between Washington and Baghdad to provide legal immunity to U.S. troops.

Last week, 170 U.S. security personnel arrived in Baghdad, including a 50-member antiterrorism team and 120 staff with helicopters and a mobile medical team. Another 100 military personnel are stationed in the region as backup.

President Barack Obama last week announced he would send as many as 300 advisers into Iraq to assess and advise Iraqi security forces.